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Statistics of chaotic tunneling

Creagh¹, Whelan

¹Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.

Physical Review Letters

|September 16, 2000

Summary

We derived the distribution of tunneling rates in chaotic systems, finding it depends on orbit stability, not universal. It matches the Porter-Thomas form for unstable orbits.

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Area of Science:

Quantum mechanics
Classical chaos
Statistical physics

Background:

Understanding quantum tunneling rates is crucial in various physical systems.
Classical chaos can significantly influence quantum phenomena like tunneling.
Previous models often assumed universality in tunneling rate distributions.

Purpose of the Study:

To derive the distribution of quantum tunneling rates in systems exhibiting classical chaos.
To investigate the dependence of this distribution on the stability of tunneling trajectories.
To explore deviations from universal distributions and their causes.

Main Methods:

Utilizing classical information on tunneling trajectories.
Applying random matrix theory arguments to wave function overlaps.
Analyzing the stability of specific tunneling orbits.

Main Results:

The derived tunneling rate distribution is not universal but depends on tunneling orbit stability.
The distribution converges to the universal Porter-Thomas form for highly unstable orbits.
Systematic deviations from universality can occur due to scarring of periodic orbits.

Conclusions:

The distribution of tunneling rates in chaotic systems is intrinsically linked to classical dynamics.
The stability of classical orbits provides a key parameter for predicting tunneling rate distributions.
Further research into orbit scarring may reveal new insights into quantum-classical correspondence.

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